In the famous paper [1]}, Huber proved a beautiful result on structures of
complete surfaces: every complete surface with integrable negative part of the Gauss curvature
is conformally equivalent to a compact surface
with a finite number of points removed.
Unfortunately, as pointed out by G. Carron and M. Herzlich in [2]}, any naive generalization of this result in higher dimensions is wrong.
Therefore, various generalizations of Huber's Theorem were obtained under some special curvature and other geometric assumptions, c.f. [3]}, [2]}, [5]}, and references
therein.
